Well‐posedness for the FENE dumbbell model of polymeric flows

Masmoudi, Nader

doi:10.1002/cpa.20252

Cited by 107 publications

(149 citation statements)

References 28 publications

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“…We do not detail the proof here (see [11]). On one hand, passing to the limit in the equation for ψ, multiplying by ψ ψ∞ and integrating in R, we get…”

Section: Idea Of the Proof Of Theorem 21mentioning

confidence: 99%

Global existence of weak solutions to some micro-macro models

Lions

Masmoudi

2007

Comptes Rendus. Mathématique

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We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution.To cite this article: A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).Key words Fokker-Planck equations, Navier-Stokes equations, FENE model, Doi model, global solutions. AMS subject classification 35Q30, 82C31, 76A05. RésuméExistence globale de solutions faibles a quelques modèles micro-macro On montre l'existence globale de solutions faiblesà certains modèles micro-macro. En particulier onétudie le modèle FENE (le cas des ressorts) et le modèle de Doi (le cas des barres rigides) La preuve est basée sur la propagation de la compacité.Pour citer cet article : A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).Version française abrégée Le modèle FENEOn montre l'existence globale de solutions faibles au modèle FENE où les polymères sont considérés comme des ressorts avec uneélongation finie. Le systéme est donné par (voir la version anglaise pour les notations).Email addresses: lions@ens.fr (P.-L. Lions), masmoudi@cims.nyu.edu (Nader Masmoudi). Preprint submitted to Elsevier Science 2 mai 2007(1) Le modèle de Doi ou modèle rigideDans le modèle de Doi, les polymères sont représentés par des barres rigides l'orientation R.On démontre le théorème suivant

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“…We do not detail the proof here (see [11]). On one hand, passing to the limit in the equation for ψ, multiplying by ψ ψ∞ and integrating in R, we get…”

Section: Idea Of the Proof Of Theorem 21mentioning

confidence: 99%

Global existence of weak solutions to some micro-macro models

Lions

Masmoudi

2007

Comptes Rendus. Mathématique

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“…The boundary conditions are homogeneous Dirichlet conditions for the velocity u plus some boundary conditions for f on Ω × ∂D(0, 1) which are implicit from the condition that f has the below defined H 1 M regularity in the q variable (we refer to [Mas08] for a discussion on the boundary conditions verified by functions in H 1 M ). We also prescribe the initial data u t=0 = u 0 and f t=0 = f 0 .…”

Section: Notations and Functional Frameworkmentioning

confidence: 99%

“…, while in [LZZ08,Mas08] it is necessary to assume that s > 2. The regularity in the q variable is also improved, roughly from H 1 to L 2 .…”

mentioning

confidence: 99%

The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

et al. 2014

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We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski diffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coefficients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.

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“…It is called the Finitely Extensible Nonlinear Elastic (FENE) connector force (see H.C. Ottinger, [34]). Some recent mathematical results about well-posedness of the FENE Fokker-Planck equation can be found in [10,26,29,39]. This is the model that we will take into account in the sequel.…”

Section: Fene Springmentioning

confidence: 99%

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

Narbona-Reina

Bresch

2013

ESAIM: M2AN

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Abstract. In this work, depending on the relation between the Deborah, the Reynolds and the aspect ratio numbers, we formally derived shallow-water type systems starting from a micro-macro description for non-Newtonian fluids in a thin domain governed by an elastic dumbbell type model with a slip boundary condition at the bottom. The result has been announced by the authors in [G. Narbona-Reina, D. Bresch, Numer. Math. and Advanced Appl. Springer Verlag (2010)] and in the present paper, we provide a self-contained description, complete formal derivations and various numerical computations. In particular, we extend to FENE type systems the derivation of shallowwater models for Newtonian fluids that we can find for instance in [J. Mathematics Subject Classification.

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Well‐posedness for the FENE dumbbell model of polymeric flows

Cited by 107 publications

References 28 publications

Global existence of weak solutions to some micro-macro models

Global existence of weak solutions to some micro-macro models

The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

Two shallow-water type models for viscoelastic flows from kinetic theory for polymers solutions

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